$\dfrac{ -2l - m }{ 7 } = \dfrac{ 10l + 3n }{ -2 }$ Solve for $l$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -2l - m }{ {7} } = \dfrac{ 10l + 3n }{ -2 }$ ${7} \cdot \dfrac{ -2l - m }{ {7} } = {7} \cdot \dfrac{ 10l + 3n }{ -2 }$ $-2l - m = {7} \cdot \dfrac { 10l + 3n }{ -2 }$ Multiply both sides by the right denominator. $-2l - m = 7 \cdot \dfrac{ 10l + 3n }{ -{2} }$ $-{2} \cdot \left( -2l - m \right) = -{2} \cdot 7 \cdot \dfrac{ 10l + 3n }{ -{2} }$ $-{2} \cdot \left( -2l - m \right) = 7 \cdot \left( 10l + 3n \right)$ Distribute both sides $-{2} \cdot \left( -2l - m \right) = {7} \cdot \left( 10l + 3n \right)$ ${4}l + {2}m = {70}l + {21}n$ Combine $l$ terms on the left. ${4l} + 2m = {70l} + 21n$ $-{66l} + 2m = 21n$ Move the $m$ term to the right. $-66l + {2m} = 21n$ $-66l = 21n - {2m}$ Isolate $l$ by dividing both sides by its coefficient. $-{66}l = 21n - 2m$ $l = \dfrac{ 21n - 2m }{ -{66} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{21}n + {2}m }{ {66} }$